From be53a5ae3a05a2232736222efd2fa548403d59ef Mon Sep 17 00:00:00 2001
From: Severino Adler <severino-adler@gmx.at>
Date: Thu, 11 Jan 2024 10:48:38 +0000
Subject: [PATCH] Update on Overleaf.

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 apssamp.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

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@@ -226,7 +226,7 @@ while no significant match with the effective \cite{Mazitov2022} Kondo temperatu
 \begin{figure}[t]
 \includegraphics[width=\linewidth]{Fig4_1.pdf}
 \includegraphics[width=\linewidth]{Fig4_2.pdf}
-\caption{\label{fig:InsulatingCoex}Phase diagrams of the MIT with PI solution in the coexistence region (blue-shaded area) for the Hubbard model (HM) on the Bethe lattice. The blue line $U_c$, taken from Ref.~\cite{Blumer2002}, denotes the thermodynamic transition. Upper panel: The data points, red squares for an insulating phase and green diamonds for a metallic phase, mark the performed DMFT calculations. The number next to the points shows the corresponding $N_{\lambda<0}$ and the background of the data points in the coexistence region shows an interpolating color scale of $N_{\lambda<0}$. Lower panel: Same phase diagram as the upper panel with approximated $\boldsymbol{\Gamma}_c^\infty$-lines of the HM, $n_{HM}$ is the number of crossed lines coming from ${U\!=\!0}$. Dashed red and orange lines (in both panels) mark the $\boldsymbol{\Gamma}_c^\infty$-lines of the Hubbard atom (HA) according to \cite{Schaefer2016} as reference, where $n_{HA}$ is the number of  $\boldsymbol{\Gamma}_c^\infty$-lines of the HA.}
+\caption{\label{fig:InsulatingCoex}Phase diagrams of the MIT with PI solution in the coexistence region (blue-shaded area) for the Hubbard model (HM) on the Bethe lattice. The blue line $U_c$, taken from Ref.~\cite{Blumer2002}, denotes the thermodynamichingegen transition. Upper panel: The data points, red squares for an insulating phase and green diamonds for a metallic phase, mark the performed DMFT calculations. The number next to the points shows the corresponding $N_{\lambda<0}$ and the background of the data points in the coexistence region shows an interpolating color scale of $N_{\lambda<0}$. Lower panel: Same phase diagram as the upper panel with approximated $\boldsymbol{\Gamma}_c^\infty$-lines of the HM, $n_{HM}$ is the number of crossed lines coming from ${U\!=\!0}$. Dashed red and orange lines (in both panels) mark the $\boldsymbol{\Gamma}_c^\infty$-lines of the Hubbard atom (HA) according to \cite{Schaefer2016} as reference, where $n_{HA}$ is the number of  $\boldsymbol{\Gamma}_c^\infty$-lines of the HA.}
 \end{figure}
 
 Our results for the PI solutions of the MIT coexistence region are shown in the upper panel of Fig.~\ref{fig:InsulatingCoex}. The two-particle calculations performed by scanning the MIT starting from the PI side are marked, respectively, with red squares or green diamonds, depending on whether a PI or a PM solution is found (the stabilization of the first PM solutions evidently corresponds to the crossing of the $U_{c1}(T)$ line).
-- 
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